• SJSU Singular Matrix Database
• Matrix group: Pothen
• Click here for a description of the Pothen group.
• Click here for a list of all matrices
• Click here for a list of all matrix groups

• Matrix: Pothen/pwt
• Description: pwt, with coordinates. From NASA, collected by Alex Pothen
• download as a MATLAB mat-file, file size: 744 KB. Use SJget(463) or SJget('Pothen/pwt') in MATLAB.
• download in Matrix Market format, file size: 592 KB.
• download in Rutherford/Boeing format, file size: 541 KB.

A singular value of A is guaranteed1 to be in the interval pictured by the blue bars around each of the calculated singular values.

Routine svds_err, version 1.0, used with Matlab 7.6.0.324 (R2008a) to calculate the 6 largest singular values and associated error bounds.
Routine spnrank, version 1.0, used with Matlab 7.6.0.324 (R2008a) to calculate singular values 35473 to 35478 and associated error bounds.

 Matrix properties (click for a legend) number of rows 36,519 number of columns 36,519 structural full rank? yes structural rank 36,519 numerical rank 35,475 dimension of the numerical null space 1,044 numerical rank / min(size(A)) 0.97141 Euclidean norm of A 9.9053 calculated singular value # 35475 4.5225e-005 numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = 6.4871e-011 calculated singular value # 35476 5.2138e-014 gap in the singular values at the numerical rank: singular value # 35475 / singular value # 35476 8.6741e+008 calculated condition number -2 condest Inf nonzeros 326,107 # of blocks from dmperm 57 # strongly connected comp. 57 entries not in dmperm blocks 0 explicit zero entries 0 nonzero pattern symmetry symmetric numeric value symmetry symmetric type binary structure symmetric Cholesky candidate? yes positive definite? no

 author NASA editor G. Kumfert, A. Pothen date 2003 kind structural problem 2D/3D problem? yes SJid 463 UFid 880

 Additional fields size and type coord full 36519-by-3

 Ordering statistics: AMD METIS DMPERM+ nnz(chol(P*(A+A'+s*I)*P')) 1,555,833 1,373,586 1,384,171 Cholesky flop count 1.6e+008 1.1e+008 1.1e+008 nnz(L+U), no partial pivoting 3,075,147 2,710,653 2,731,823 nnz(V) for QR, upper bound nnz(L) for LU 2,667,503 2,280,757 2,306,405 nnz(R) for QR, upper bound nnz(U) for LU 5,000,519 4,300,180 4,338,203

Maintained by Leslie Foster, last updated 24-Apr-2009.

Entries 5 through 14 in the table of matrix properties and the singular
value plot were created using SJsingular code. The other plots
and statistics are produced using utilities from the SuiteSparse package.
Matrix color plot pictures by cspy, a MATLAB function in the CSparse package.